MAIN GOAL (?): Any physics Feynman-diagram complex amplitude (or perhaps |amplitude|^2 or something?) can be written as the volume of a certain polytope in an infinite dimensional space
The fact that Arkani-Hamed's polytope is "in an infinite dimensional space" seems however to exclude any such algorithm, the above results were in finite dimensional spaces.
--actually the usual Feynman diagram formulation yields an algorithm to evaluate any diagram to within epsilon via numerical integration, which I think can be shown to be in the complexity class #P. But the infinite-dimensional polytope formulation (if any) does not seem to lead to any algorithm at all. If the dimension can be made finite, then there would be an algorithm. So on the face of it, this seems a step in the wrong direction. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)